AFastandAccurateTwoOrdersofScatteringModeltoAccountfor一个快速和准确的二阶散射模型来解释

1、.A13B-0915: A Fast and Accurate Two Orders of Scattering Model to Account for Polarization in Trace Gas Retrievals From Satellite MeasurementsVijay Natraj1,*, Robert J.D. Spurr2, Hartmut Bösch3 and Yuk L. Yung11 MC 150-21, Division of Geological and Planetary Sciences, California Institute of T

2、echnology, 1200 E California Blvd, Pasadena, CA 91125, USA2 RT Solutions Inc., 9 Channing St., Cambridge, MA 02138, USA3 Jet Propulsion Laboratory, California Institute of Technology, MS 183-601, 4800 Oak Grove Dr, Pasadena, CA 91109, USAIntroductionSatellite measurements have been playing a major r

3、ole in weather and climate research for the fast few decades. For most applications, interpretation of such measurements requires an accurate modeling of the atmosphere and surface. Typically, trace gas retrieval algorithms are simplistic because of computer resource and time considerations. In part

4、icular, they neglect polarization effects due to the surface, atmosphere and instrument. This can cause significant errors in retrieved trace gas column densities, particularly in the ultraviolet (UV) and near infrared (NIR) spectral regions because of appreciable scattering by air molecules, aeroso

5、ls and clouds. On the other hand, it has been shown 1, for example, that retrieving the sources and sinks of CO2 on regional scales requires the column density to be known to 1-2 ppm (0.3-0.5%) precision. Clearly, radiative transfer (RT) models need to be developed to achieve such precisions, while

6、working at speeds necessary to meet operational needs.Proposed Solution: Two Orders of Scattering to Compute PolarizationMultiple scattering is known to be depolarizing. It follows, then, that the major contribution to polarization comes from the first few orders of scattering. Ignoring polarization

7、 leads to two kinds of errors. The first kind is errors due to the neglect of the polarized components of the Stokes vector. The second kind is the errors in the intensity itself from not accounting for polarization. The simplest (and fastest) approximation for polarization would clearly be single s

8、cattering. However, for unpolarized incident light (such as sunlight), single scattering does not account for polarization effects on the intensity. On the other hand, three (and higher) orders of scattering, while giving highly accurate results, involve nearly as much computation as a full multiple

9、 scattering calculation. It would thus appear that two orders of scattering is optimal.We calculate the reflection matrix for the first two orders of scattering (2OS) in a vertically inhomogeneous, scattering-absorbing medium. We take full account of polarization, and perform a complete linearizatio

10、n (analytic differentiation) of the reflection matrix with respect to both the inherent optical properties of the medium and the surface reflection condition. Further, we compute a scalar-vector correction to the total intensity due to the effect of polarization; this correction is also fully linear

11、ized. The intensity correction is meant to be combined with a scalar intensity calculation (with all orders of scattering included) to approximate the intensity with polarization effects included. An approximate spherical treatment is given for the solar and viewing beam attenuation, enabling accura

12、te computations for the range of viewing geometries encountered in practical radiative transfer applications.The following equation summarizes the approach:where Isca and Icor refer to the scalar intensity with polarization neglected but all orders of scattering accounted for and the scalar-vector i

13、ntensity correction computed using our approach, respectively; the subscript 2OS indicates results calculated using the 2OS model.Scenarios to Test Proposed TechniqueWe use the spectral regions to be measured by the Orbiting Carbon Observatory (OCO) mission 2 to test the 2OS model. Six different loc

14、ations and two different seasons have been considered (see Fig. 1 for geographical location map), with four different aerosol loadings (0.01, 0.05, 0.1, 0.2) for each of the above.Surface CO2, July 1, 12 UTPark Falls (46 N, 90.3 W)South Pacific (30 S, 210 E)Darwin (12 S, 130 E)Lauder (45 S, 170 E)Ny

15、 Alesund (79 N, 12E)Algeria (30 N, 8 E)Figure 1: Geographical Location of Test SitesThe details of the geometry, surface type and tropospheric aerosol type 3 for the various scenarios are summarized in Table 1. The stratospheric aerosol has been assumed to be a 75% solution of H2SO4 with a modified

16、gamma size distribution 4.Solar Zenith Angle (degrees)Surface TypeAerosol Type (Kahn Grouping)Algeria Jan157.48DesertDusty Continental (4b)Algeria Jul 121.03DesertDusty Continental (4b)Darwin Jan 123.24DeciduousDusty Maritime (1a)Darwin Jul 141.44DeciduousBlack Carbon Continental (5b)Lauder Jan 134.

17、22GrassDusty Maritime (1a)Lauder Jul 174.20FrostDusty Maritime (1b)Ny Alesund Apr 180.77SnowDusty Maritime (1b)Ny Alesund Jul 162.43GrassDusty Maritime (1b)Park Falls Jan 172.98SnowBlack Carbon Continental (5a)Park Falls Jul 131.11ConiferDusty Continental (4b)South Pacific Jan 124.62OceanDusty Marit

18、ime (1a)South Pacific Jul 158.84OceanDusty Maritime (1b)Table 1: Scenario DetailsResidualsThe spectral residuals have been plotted for two scenarios, Algeria Jul 1 (aerosol od 0.01) and Ny Alesund Apr 1 (aerosol od 0.2), which represent the best and worst case, respectively (see Figs. 2 and 3). The

19、blue, green and red lines in the top panel refer to the vector, scalar, and 2OS results, respectively. The middle and bottom panels show the radiance errors using scalar and 2OS models, respectively. For the former case, the low solar zenith angle and relatively high surface albedos combine to reduc

20、e the polarization. The latter case is one of high solar zenith angle and a surface that is extremely bright in the O2 A band and extremely dark in the CO2 bands. This explains the high continuum polarization in the CO2 bands. Nevertheless, the 2OS model improves the residuals by an order of magnitu

21、de in the worst case and more than two orders of magnitude in the best case. The rms residuals are plotted for all the scenarios in Figs. 4 and 5. Figure 2: Spectral Residuals for Algeria Jul 1 (Aerosol OD 0.01) ScenarioFigure 3: Spectral Residuals for Ny Alesund Apr 1 (Aerosol OD 0.2) ScenarioFigur

22、e 4: RMS Residuals (Scalar)Figure 4: RMS Residuals (2OS)Sensitivity StudiesIt is more instructive to understand the effect of the approximation on the errors in the retrieved CO2 column. These errors can be assessed by performing a linear error analysis study 5,6. Forward model errors are typically

23、systematic and result in a bias in the retrieved parameters x. This bias can be expressed as:where G is the gain matrix that represents the mapping of the measurement variations into the retrieved vector variations and DF is the error in the modeling made by the scalar (or 2OS) approximation.where I

24、calc is the calculated quantity, and is equal to Isca for the scalar model and Isca + Icor Q2OS for the 2OS model. All the quantities are vectors over the detector pixels.The measurement and smoothing errors and the error due to the scalar and 2OS approximations are summarized in Table 2. Clearly, t

25、he errors due to the 2OS approximation are smaller or of the same order of magnitude than the noise and smoothing errors even in the worst case (in most cases, it is at least an order of magnitude smaller). On the other hand, the reverse situation is true if polarization is ignored.ScenarioMeasureme

26、nt Error (ppm)Scalar Error (ppm)2OS Error(ppm)Smoothing Error (ppm)Algeria Jul 10.320.420.00270.25Ny Alesund Apr 14.26136.374.134.11Table 2: Summary of ErrorsConclusionsSensitivity studies were performed to evaluate the errors resulting from using a novel approximation to compute polarization in sim

27、ulations of backscatter measurements of spectral bands by space-based instruments such as that on OCO. It was found that the errors in the top of the atmosphere (TOA) radiance were less than 0.1% in most cases. The computation time was two orders of magnitude less than that for an exact vector computation. A linear error analysis study of simulated measurements from the OCO absorption bands shows that errors due to the 2OS approximation are much lower than the smoothing and measurement noise errors. This is in contrast to the